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0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 342 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 348 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 349 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 350 1 {CSTYLE "" -1 -1 " Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 355 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 356 1 {CSTYLE "" -1 -1 "Times" 0 1 178 0 40 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 357 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 375 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 376 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 377 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 378 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 15 379 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 15 380 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 15 381 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 386 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 387 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 388 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 389 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 390 1 {CSTYLE "" -1 -1 " Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 391 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 392 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 393 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 394 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 395 1 {CSTYLE "" -1 -1 " Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 396 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 1 {PARA 386 "" 0 "" {TEXT 349 19 " Basic Interaction" } }{PARA 386 "" 0 "" {TEXT 350 84 "The symbol \">\" is Maple's command p rompt. At the command prompt you type a command " }{TEXT 354 44 "foll owed by a either a semi-colon or a colon" }{TEXT 355 15 ". Hitting th e " }{TEXT 352 5 "Enter" }{TEXT 353 464 " key will then execute the co mmand. It is important to remember that each command is terminated by a colon or semi-colon. When you use the semicolon, Maple will show yo u the output of the command. When you use the colon, Maple will do th e calculation but suppress the output. This is useful if the calculat ion has a lengthy output that you don't need to see. For example, her e is a simple sequence of Maple commands. Place the cursor on each on e and try them." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "a := (x+3 )^2*(x-1)^5*(x+11);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expa nd(a);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 261 "" 0 "" {TEXT 280 2 " " } {TEXT 358 10 "Arithmetic" }}{PARA 262 "" 0 "arithmetic" {TEXT 281 292 "First, there is arithmetic: addition, subtraction, multiplication, di vision and exponentiation. These can be combined, just as on a calcula tor. The order of precedence is the the usual one: exponentiation fi rst, then multiplication and division, then addition and subtraction. \+ So entering " }}{EXCHG {PARA 263 "> " 0 "" {MPLTEXT 1 0 13 " 2-3+4/5* 6^7;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "(2-3)+(4/5)*(6^7); \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "1/3 + 1/2;\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "1./3+1/2;\n" }}}{EXCHG {PARA 269 "> " 0 "" {MPLTEXT 1 0 15 "evalf(1/2+1/3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "(3+2*I)*(2-I);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Pi*3^2;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "(2^30/3^20)*sqrt(3); evalf(%);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "100!;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "if actor(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "exp(1); " }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(%,50);" }}}}{SECT 1 {PARA 273 "" 0 "" {TEXT 288 2 " " }{TEXT 361 1 "E" }{TEXT 360 45 "xpr essions, names, statements and assignments" }}{PARA 274 "" 0 "expressi ons" {TEXT 273 52 " Quantities to be computed like 1/2+1/3 are called \+ " }{TEXT 257 11 "expressions" }{TEXT 362 7 " . A " }{TEXT 363 4 "na me" }{TEXT 364 88 " is a string of characters which can be used to st ore the result of a computation. A " }{TEXT 365 9 "statement" } {TEXT 271 179 " in Maple is a string of names and expressions termina ted with a semicolon, or a colon if you don't want to see the output , which when entered will produce some action. The " }{TEXT 366 10 "assignment" }{TEXT 272 68 " statement is one of the most common sta tements. It has the form " }{TEXT 367 17 "name := expresion" }{TEXT 368 31 ". For example , the assignment" }}{EXCHG {PARA 275 "> " 0 "" {MPLTEXT 1 0 15 "area := Pi*3^2;" }}}{PARA 276 "" 0 "" {TEXT 289 20 "s tores the value 9*" }{XPPEDIT 18 0 "Pi" "6#%#PiG" }{TEXT 369 35 " in a location marked by the name " }{TEXT 373 4 "area" }{TEXT 374 1 "." }}{PARA 277 "" 0 "" {TEXT -1 0 "" }}{PARA 277 "" 0 "" {TEXT 290 53 "A \+ more useful assignment for the area of a circle is " }}{EXCHG {PARA 278 "> " 0 "" {MPLTEXT 1 0 15 "area := Pi*r^2;" }}}{PARA 279 "" 0 "" {TEXT 291 18 "In this case, the " }{TEXT 370 10 "expression" }{TEXT 371 3 " " }{XPPEDIT 18 0 "Pi" "6#%#PiG" }{TEXT 372 19 "*r^2 is stor ed in " }{TEXT 375 4 "area" }{TEXT 376 105 " and with this assignment, the area of a circle of any given radius can be computed using the Ma ple word " }{TEXT 377 4 "subs" }{TEXT 378 50 ". So to calculate the a rea when r is 3, we enter " }}{EXCHG {PARA 280 "> " 0 "" {MPLTEXT 1 0 15 "subs(r=3,area);" }}}{PARA 281 "" 0 "function" {TEXT 292 80 "Here, \+ it is convenient to think of the assignment as defining area as a func tion" }}{PARA 282 "" 0 "" {TEXT 274 2 " o" }{TEXT 293 15 "f the radius r." }{TEXT 275 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} }{SECT 1 {PARA 283 "" 0 "" {TEXT 258 2 " " }{TEXT 294 9 "Functions" } {TEXT 381 1 " " }{TEXT 382 15 "and expressions" }}{PARA 284 "" 0 "" {TEXT 295 311 "Maple makes a careful distinction between and expressio n and a function. This distinction can sometimes cause confusion when you first begin to use Maple. Some Maple commands work on expression s but not functions, others work on functions but not expressions, oth ers work on both but require different syntax." }}{PARA 285 "" 0 "expr ession" {TEXT 296 1 " " }}{PARA 285 "" 0 "" {TEXT 383 16 "The assignme nt " }}{EXCHG {PARA 286 "> " 0 "" {MPLTEXT 1 0 15 "f := x^3-5*x+1;" } }}{PARA 287 "" 0 "" {TEXT 297 11 "stores the " }{TEXT 384 10 "expressi on" }{TEXT 385 1 " " }{XPPEDIT 18 0 "x^3-5*x+1;" "6#,(*$%\"xG\"\"$\"\" \"*&\"\"&F'F%F'!\"\"F'F'" }{TEXT 386 23 " in the location named " } {TEXT 388 1 "f" }{TEXT 389 46 ". If we try to use functional notation like " }{TEXT 390 1 "f" }{TEXT 391 110 "(3) to substitute 3 for x, M aple doesn't do what we want it to. Put the cursor on the lie below a nd try it. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(3);" }}} {PARA 288 "" 0 "" {TEXT -1 27 "Instead we need to use the " }{TEXT 387 4 "subs" }{TEXT -1 44 " command mentioned in the previous section. " }}{EXCHG {PARA 289 "> " 0 "" {MPLTEXT 1 0 12 "subs(x=3,f);" }}} {PARA 290 "" 0 "" {TEXT -1 44 "However, we can differentiate and integ rate " }{TEXT 395 1 "f" }{TEXT -1 51 " because these Maple commands ap ply to expressions." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff( f,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(f,x);" }}} {PARA 291 "" 0 "" {TEXT -1 18 "We can also graph " }{TEXT 396 1 "f" } {TEXT -1 27 " over a specified interval." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot(f, x=-5..5);" }}}{PARA 292 "" 0 "" {TEXT 298 1 " " }}{PARA 0 "" 0 "" {TEXT -1 37 "Maple defines functions by using the " }{TEXT 392 15 "arrow operator." }}{EXCHG {PARA 293 "> " 0 "" {MPLTEXT 1 0 20 "g := x -> x^3-5*x+1;" }}}{PARA 294 "" 0 "" {TEXT -1 20 "Now we can evaluate " }{TEXT 394 1 "g" }{TEXT -1 30 " by using fun ctional notation." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(3);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "diff_quotient := (g(x+h)-g(x))/h;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "limit(diff_quotient,h=0);" }}} {PARA 295 "" 0 "" {TEXT -1 27 "If we try to differentiate " }{TEXT 393 1 "g" }{TEXT -1 17 " with the command" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(g,x);" }}}{PARA 0 "" 0 "" {TEXT -1 40 "we get a surprising result because the " }{TEXT 397 4 "diff" }{TEXT -1 59 " co mmand only works on expressions. The correct command is" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "D(g);" }}}{PARA 387 "" 0 "" {TEXT 398 97 "Notice how the result is another function. So to get the deri vative of g at x = -2, we would use" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "D(g)(-2);" }}}{PARA 387 "" 0 "" {TEXT 401 104 "To plot the function over the interval -5..5, we can use the following comman d. Note that the variable " }{TEXT 400 1 "x" }{TEXT 399 19 " is omitt ed here. " }}{EXCHG {PARA 388 "> " 0 "" {MPLTEXT 1 0 14 "plot(g,-5..5 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 296 "" 0 "" {TEXT 259 2 " " }{TEXT 402 54 "Built in Maple functions a nd operations with functions" }}{PARA 297 "" 0 "" {TEXT 299 78 " All o f the standard scientific functions are built into Maple. For example , " }{TEXT 403 4 "sqrt" }{TEXT 404 33 " is the square root function, \+ " }{TEXT 405 3 "abs" }{TEXT 406 74 " is the absolute value function , the trig and inverse trig functions are " }{TEXT 407 3 "sin" }{TEXT 408 2 ", " }{TEXT 410 6 "arcsin" }{TEXT 409 2 ", " }{TEXT 411 3 "cos" }{TEXT 412 60 ", etc., the natural logarithm and exponential functions are " }{TEXT 413 2 "ln" }{TEXT 414 6 " and " }{TEXT 415 3 "exp" } {TEXT 416 52 " . For a complete list of built in functions, type " }} {EXCHG {PARA 298 "> " 0 "" {MPLTEXT 1 0 9 "?inifcns " }}}{PARA 299 "" 0 "" {TEXT -1 0 "" }}{PARA 300 "" 0 "composition" {TEXT 300 256 " New \+ functions can be obtained from old functions by use of the arithmetic \+ operations of addition, subtraction, multiplication, and division toge ther with the operation of composition, which is denoted by @ . Thu s the function defined by the assignment " }}{EXCHG {PARA 301 "> " 0 " " {MPLTEXT 1 0 21 "y := sin(cos(x^2+3));" }}}{PARA 302 "" 0 "" {TEXT 301 28 " and evaluated at x=3 by " }}{EXCHG {PARA 303 "> " 0 "" {MPLTEXT 1 0 13 "subs(x=3.,y);" }}}{PARA 304 "" 0 "" {TEXT 302 39 "cou ld also be defined by the assignment" }}{EXCHG {PARA 305 "> " 0 "" {MPLTEXT 1 0 24 "y := sin@cos@(x->x^2+3);" }}}{PARA 306 "" 0 "" {TEXT 303 28 " and evaluated at x=3 by" }}{EXCHG {PARA 307 "> " 0 "" {MPLTEXT 1 0 6 "y(3.);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 " Gra phing" }}{PARA 0 "" 0 "" {TEXT -1 171 "Maple has an extensive set of c ommands for producing graphs of all sorts. What follows is a sampler \+ of the more basic commands. Most of these examples are taken form the " }{TEXT 429 24 " Maple Learning Guide. " }{TEXT -1 152 "The Help fac ility described in a section below also has a complete description of \+ each command and its variations. I urge you to browse and experiment. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 81 "To pl ot a function, you need to supply the function or expression and the d omain." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "f := 7*sin(x)+sin( 7*x);\nplot(f,x=-3*Pi..3*Pi);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 55 "You can also specify the range along the \+ vertical axis." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(f,x=- 3*Pi..3*Pi,y=0..10);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 53 "This is useful for zooming in on detail. For example, " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(tan(x),x=-2*Pi..2*P i);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "N ow restrict the range to y between -4 and 4. The more familiar pictur e now appears." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot(tan(x ),x=-2*Pi..2*Pi,y=-4..4);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 103 "The tangent function has discontinuities and Map le draws nearly vertical lines near these points. The " }{TEXT 433 7 "discont" }{TEXT -1 25 " option eliminates these." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "plot(tan(x),x=-2*Pi..2*Pi, y=-4..4, discont=t rue);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "Multiple plots on the same axes are also possible." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "plot(\{x,x^2,x^3\}, x=-3..3,y=-10..10);" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "Here is \+ an example of a parametric plot" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot([cos(t),sin(t),t=0..2*Pi]);" }}}{PARA 0 "" 0 "" {TEXT -1 307 "The graph should be a circle. It may look elliptical because Map le scales the graph to fit the window. Try resizing the graph window \+ and observe how the shape changes. The following option will insure t hat the graph appears circular. Execute the following command and the n try resizing the graph window." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "plot([cos(t),sin(t),t=0..2*Pi], scaling=CONSTRAINED);" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "You can p lot a list of data points. (Lists in Maple are covered in a later sec tion.)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "data := [[-3,9],[- 2,4],[-1,1],[0,0],[1,5]];\nplot(data);\n" }}}{PARA 0 "" 0 "" {TEXT -1 53 "If you don't want the points to be connected use the " }{TEXT 434 5 "style" }{TEXT -1 8 " option." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot(data, style=POINT);" }}}{PARA 0 "" 0 "" {TEXT -1 68 "You \+ can also change the symbol used by Maple to indicate the points." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "### WARNING: the definition of the type `symbol` has changed'; see help page for details\nplot(da ta, style=POINT, symbol=DIAMOND);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 43 "Here is an example of a 3 dimensional plo t." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot3d(x*(x^2-3*y^2), \+ x=-1..1, y=-1..1);" }}}{PARA 0 "" 0 "" {TEXT -1 245 "The help facility describes a whole range of options for 3d plots. Many of these optio ns can be selected form the menu bar associated with a graph window, o r they can also be specified directly in the command line. Here are th ree common ones. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "plot3d (x*(x^2-3*y^2), x = -1..1, y = -1..1, orientation = [58, 73], axes=BOX ED, style=PATCH);" }}}{PARA 0 "" 0 "" {TEXT -1 39 "Multiple plots are \+ also possible in 3d." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "plot 3d(\{2-x+y,x+y-1,3-x-1\},x=-10..10,y=-10..10,orientation=[40, 70], axe s=BOXED);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 219 "The examples in thi s section are only the tip of the iceberg with regard to Maple's graph ics commands. Many of these commands are contained in a separate pack age which can be loaded by invoking the following command. " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "The help facility describes these command s and gives examples. Experiment on your own!" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 417 19 " S olving equations" }}{PARA 3 "" 0 "" {TEXT 418 70 "You can use Maple to solve equations exactly. Here are some examples:" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 21 "solve(x^3-13*x+12,x);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 19 "solve(\{x^2=4\},\{x\});" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 54 "eqn := x^3-1/2*a*x^2+13/3*x^2 = 13/6*a*x+10/3* x-5/3*a;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solve( eqn, \{x \} );" }}}{PARA 0 "" 0 "" {TEXT -1 51 "You can also solve systems of e quations in Maple. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "solv e(\{x+2*y=3,y+1/x=1\}, \{x,y\});" }}}{PARA 0 "" 0 "" {TEXT -1 59 "Here is an example consisting of 5 equations in 5 unknowns." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "eqn1 := a+2*b+3*c+4*d+5*e=41;\neqn 2 := 5*a+5*b+4*c+3*d+2*e=20;\neqn3 := 3*b+4*c-8*d+2*e=125;\neqn4 := a+ b+c+d+e=9;\neqn5 := 8*a+4*c+3*d+2*e=11;\n" }}}{PARA 0 "" 0 "" {TEXT -1 44 "Now solve the system for all the variables, " }{XPPEDIT 18 0 "a " "6#%\"aG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "b" "6#%\"bG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "c" "6#%\"cG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "d" "6#%\"dG" }{TEXT -1 6 ", and " }{XPPEDIT 18 0 "e" "6#%\"eG" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "solve( \{eqn1, eqn2, eqn3, eqn4, eqn5\}, \{a, b, c, d, e\} );" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Maple also has a command " } {TEXT 420 6 "fsolve" }{TEXT -1 109 " for solving numerically. This co mmand uses a variation of Newton's method to produce approximate solut ions." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "fsolve(\{cos(x)=x\} ,\{x\});" }}}{PARA 0 "" 0 "" {TEXT -1 12 "In general, " }{TEXT 419 6 " fsolve" }{TEXT -1 98 " searches for a single real root. For polynomia l equations, however, it looks for all real roots." }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 32 "p := 3*x^4-16*x^3-3*x^2+13*x+16;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "fsolve(\{p\},\{x\});" }}}{PARA 0 " " 0 "" {TEXT -1 30 "You can ask for complex roots." }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 24 "fsolve(\{p\},\{x\},complex);" }}}{PARA 0 "" 0 "" {TEXT -1 28 "You can also restrict where " }{TEXT 421 6 "fsolve" }{TEXT -1 19 " looks for roots. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "fsolve(\{p\},x=0..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 389 "" 0 "" {TEXT 422 2 " " } {TEXT 428 59 "A quick example: using Maple as a fancy graphing calcula tor" }}{PARA 390 "" 0 "" {TEXT 423 161 "It is convenient to think of M aple as a fancy graphing calculator for many purposes. For example, s uppose you want to find the real solutions of the equation " } {XPPEDIT 18 0 "x^5-30*x-2 = 0" "6#/,(*$%\"xG\"\"&\"\"\"*&\"#IF(F&F(!\" \"\"\"#F+\"\"!" }{TEXT 424 20 " in the interval " }{XPPEDIT 18 0 "- 3..3" "6#;,$\"\"$!\"\"F%" }{TEXT 425 58 " . First we can plot the rig ht hand side of the equation." }}{EXCHG {PARA 391 "> " 0 "" {MPLTEXT 1 0 20 "f := 10*x^5-30*x+10;" }}}{EXCHG {PARA 392 "> " 0 "" {MPLTEXT 1 0 16 "plot(f,x=-3..3);" }}}{PARA 393 "" 0 "" {TEXT 426 61 "By inspec tion, the graph crosses near 0. We can look closer." }}{EXCHG {PARA 394 "> " 0 "" {MPLTEXT 1 0 31 "plot(f,x=-1.5..1.5,y=-20..40); " }}} {PARA 395 "" 0 "" {TEXT 427 161 " We see that the graph crosses 3 time s, the largest solution being between 1 and 1.5. If we wanted the la rgest solution more accurately, we could use fsolve . " }}{EXCHG {PARA 396 "> " 0 "" {MPLTEXT 1 0 21 "fsolve(f=0,x=1..1.5);" }}}}{SECT 1 {PARA 308 "" 0 "" {TEXT 304 2 " " }{TEXT 442 37 "Expression sequenc es, lists and sets." }{TEXT 443 2 " " }}{PARA 309 "" 0 "" {TEXT 305 128 "Maple has a variety of data structures for representing informati on. This section describes three of the most important ones. \n" }} {PARA 309 "" 0 "" {TEXT 444 3 "An " }{TEXT 445 19 "expression sequence " }{TEXT 446 67 " is any sequence of expressions separated by commas. \+ For example, " }}{EXCHG {PARA 310 "> " 0 "" {MPLTEXT 1 0 50 "expseq : = 1,2, w*r+m, a=b+c, 1/2, (x+y)/z,`hello`;" }}}{PARA 311 "" 0 "" {TEXT 306 33 "is an assignment to the variable " }{TEXT 447 6 "expseq " }{TEXT 448 48 " a sequence of 7 expressions. To refer to the " }} {PARA 312 "" 0 "" {TEXT 307 62 "sixth expression in this sequence, us e the following command." }}{PARA 313 "> " 0 "" {MPLTEXT 1 0 11 "expse q[6]; " }}{PARA 0 "" 0 "" {TEXT -1 52 "You can also create an expressi on sequence with the " }{TEXT 449 3 "seq" }{TEXT -1 9 " command." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "squares := seq(i^2,i=1..10); " }}}{PARA 314 "" 0 "" {TEXT -1 0 "" }}{PARA 314 "" 0 "" {TEXT 308 3 " A " }{TEXT 450 4 "list" }{TEXT 451 69 " is an expression sequence enc losed by square brackets. For example, " }}{EXCHG {PARA 315 "> " 0 "" {MPLTEXT 1 0 15 "L := [squares];" }}}{PARA 316 "" 0 "" {TEXT 309 190 " As with expression sequences, we can refer to particular terms of a li st by appending to its name the number of the term enclosed in square \+ brackets. Thus to get the fifth term of the list " }{TEXT 454 1 "L" } {TEXT 455 22 " , type the expression" }}{EXCHG {PARA 317 "> " 0 "" {MPLTEXT 1 0 5 "L[5];" }}}{PARA 318 "" 0 "" {TEXT 310 60 "You can also reference the fifth term in this list by typing" }}{EXCHG {PARA 319 " > " 0 "" {MPLTEXT 1 0 8 "op(5,L);" }}}{PARA 320 "" 0 "" {TEXT 311 52 " To count how many terms are in a list, use the word " }{TEXT 452 4 "no ps" }{TEXT 453 19 " . So for example," }}{EXCHG {PARA 321 "> " 0 "" {MPLTEXT 1 0 8 "nops(L);" }}}{PARA 322 "" 0 "" {TEXT 312 45 "tells us \+ that there are 10 terms in the list " }{TEXT 456 1 "L" }{TEXT 457 8 " \+ . The " }{TEXT 458 4 "nops" }{TEXT 459 33 " command comes in handy w hen you" }}{PARA 323 "" 0 "" {TEXT 313 325 "don't want to (or can't) c ount the terms in a list by hand (this is almost always). You can't di rectly use the word nops to count the number of terms in an express ion sequence. But you can put square brackets around the expression \+ sequence and count the terms in the resulting list. This device is us ed again and again." }}{EXCHG {PARA 324 "> " 0 "" {MPLTEXT 1 0 12 "nop s(3,4,a);" }}}{EXCHG {PARA 325 "> " 0 "" {MPLTEXT 1 0 14 "nops([3,4,a] );" }}}{PARA 326 "" 0 "" {TEXT 314 3 "\nA " }{TEXT 460 3 "set" }{TEXT 461 185 " is an expression sequence enclosed by curly brackets. Order of appearance is not important in sets. Sets are important when plo tting more than one function at at time. For example," }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 327 "" 0 "" {TEXT 260 2 " " }{TEXT 462 25 "Maple control statements " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 332 "> " 0 "" {MPLTEXT 1 0 46 " s := 0: for i from 1 to 100 do s := s+i od:" }}} {EXCHG {PARA 333 "> " 0 "" {MPLTEXT 1 0 3 " s;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "locube := []: # start with the empty list\n for i from 1 to 5 do \n locube := [op(locube),i^3] od: \nlocube ; # look at the list; \n" }}}{EXCHG {PARA 342 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "aocube := array(1..5): # initialize the ar ray.\n" }}}{EXCHG {PARA 348 "> " 0 "" {MPLTEXT 1 0 43 "for i from 1 to 5 do aocube[i]:= i^3 od; " }}}{EXCHG {PARA 349 "> " 0 "" {MPLTEXT 1 0 33 " op(aocube); # to see the array " }}}{EXCHG {PARA 350 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "aocu be[3]:=0;\n" }}}{EXCHG {PARA 355 "> " 0 "" {MPLTEXT 1 0 14 "print(aocu be);" }}}{EXCHG {PARA 356 "> " 0 "" {MPLTEXT 1 0 54 "locube := [locube [1],locube[2],0,locube[4],locube[5]];" }}}{EXCHG {PARA 357 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "myabs := proc(x) if x > 0 th en x else -x fi end;\n" }}}{EXCHG {PARA 375 "> " 0 "" {MPLTEXT 1 0 11 "myabs(-23);" }}}{EXCHG {PARA 376 "> " 0 "" {MPLTEXT 1 0 94 "plot(myab s,-2..2,scaling=constrained,title=`my absolute value`); # to see what it looks like." }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 25 " The Maple \+ Help facility" }}{PARA 0 "" 0 "" {TEXT -1 194 "As mentioned earlier Ma ple has a well designed on-line help system complete with descriptions and executable examples of all the Maple commands. There are several different ways to access help." }}{PARA 15 "" 0 "" {TEXT -1 55 "Pull \+ down the help menu on the menu bar and choose the " }{TEXT 435 9 "Cont ents " }{TEXT -1 250 "option. What comes up is a window that will let you browse through the system via hyperlinks. These are the green un derlined entries. Clicking on one of these will take you to that page . In this way you can move quickly through the help database." }} {PARA 15 "" 0 "" {TEXT -1 73 "If you now the topic or almost know the \+ name of the command, then choose " }{TEXT 436 12 "Topic Search" } {TEXT -1 214 " from the help menu and type in the name of the command. As you type, Maple will display a list of the command that start wit h the letters you've typed. This is great if you don't quite know the complete command." }}{PARA 15 "" 0 "" {TEXT -1 43 "If you know the na me of the command typing " }{TEXT 438 8 "?command" }{TEXT -1 65 " will bring up the help page for that command. For example, try " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?plot" }}}{PARA 15 "" 0 "" {TEXT -1 61 "If you don't know the name of the command, but you can tr y a " }{TEXT 437 16 "Full Text Search" }{TEXT -1 152 " from the help m enu. Type in a few key words that describe the command or that you th ink might appear on the help page for the command you are seeking." }} {PARA 15 "" 0 "" {TEXT -1 65 "Nearly all of the help pages have hyperl inks to related topics. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 341 2 " " }{TEXT 430 22 "Trouble \+ Shooting Notes" }}{PARA 377 "" 0 "trouble shooting" {TEXT 342 365 "Lea rning to use Maple can be an extremely frustrating experience, if you \+ let it. There are some types of errors which occur from the beginning that can be spotted and corrected easily by a person fluent in Maple, so if you have access to such a person, use them. Here are a few sug gestions that may be of use when you're stuck with a worksheet that's \+ not working." }}{PARA 378 "" 0 "" {TEXT 343 2 " " }}{PARA 379 "" 0 " " {TEXT 344 10 " Use the " }{TEXT 431 4 "help" }{TEXT 432 245 " facil ity: There is a help sheet with examples for every Maple word. \nA q uick read through will often clear up syntax problems. One very commo n early mistake is to leave out the parentheses around the inputs of a word. For example, typing " }{MPLTEXT 1 0 10 "plot x^2; " }{TEXT 345 66 "will get you a syntax error, because you left out the parenthe ses." }}{PARA 380 "" 0 "" {TEXT 346 151 " The Maple command prompt i s \">\". You can begin entering input after it. Make sure you are t yping into an input cell, if you are expecting output." }}{PARA 381 " " 0 "" {TEXT 347 186 " End Maple statements with a semicolon. Maple does nothing until it finds a semicolon. If you are getting no outpu t when you should be, try feeding in a semicolon. This often works." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 30 " Other sources of information " }}{PARA 0 "" 0 "" {TEXT -1 52 "Books (there are hundreds of them). \+ Here are a few." }}{PARA 15 "" 0 "" {TEXT -1 24 "Heal, Hansen and Rick ard" }{TEXT 439 28 ", The Maple V Learning Guide" }{TEXT -1 25 ", Spr inger Verlag, 1996." }}{PARA 15 "" 0 "" {TEXT -1 21 "Wade Ellis, et. a l., " }{TEXT 440 25 "The Maple V Flight Manual" }{TEXT -1 20 ", Brooks Cole, 1992." }}{PARA 15 "" 0 "" {TEXT -1 12 "Andre Heck, " }{TEXT 441 22 " Introduction to Maple" }{TEXT -1 112 ", Springer Verlag, 1993 . (This one covers an Release 3. It may be available in a newer vers ion for Release 4.)" }}{PARA 0 "" 0 "" {TEXT -1 96 "Internet sites (th ere are hundreds of them, maybe more). The following are good places \+ to start" }}{PARA 15 "" 0 "" {TEXT -1 0 "" }}}}{MARK "5" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }